This is the big problem with most (all?) commercial "Internet of Things" devices. It's a real mess, and that is because this idea is unworkable from the start. What we should have instead are many, isolated "Intranets of Things".
Of course, you should build your own bridge to connect them to (rather than using the bridge of a big tech company).
For Zigbee you can use the Conbee [0] and for Z-Wave you can use the Z-Stick [1] to build your own bridge.
Furthermore, some of the cheaper WiFi devices that are based on the ESP8266 chip can be flashed with a custom firmware called Tasmota [2] to make them cloud-free.
[0]: https://www.phoscon.de/en/conbee2
Devices based on the popular ESP8266 can also frequently be freed from their cloud overlords with community-made firmware [0], [1] and used as proper Intra-o-T devices.
I decided a while back that I would have no part in this Inter-o-T madness and I think it was a good choice.
[0]: https://github.com/arendst/Tasmota
[1]: https://esphome.io/
Heh, just noticed you linked Tasmota as well while I was writing this. Good project, I use it too!
If both the phone and the device are in the same network, they can communicate just fine.
I dumped my Wink Hub for one after they did their bait-and-switch for subscription fees. Never been happier with home automation.
Nah, Internet is great for updates.
The problem, while it doesn't fit a description as slogan-friendly as yours, is the reliance on centralized servers as essential for routine operations rather than just for optional (though potentially important) updates, and this isn’t an engineering problem but a deliberate business decision to enable X-as-a-Service business models (whether paid for via recurring subscription, ongoing user data, or both.)